May I ask what highway number that is?
This past week we towed over Monarch Pass, at 11,310 feet, on US 50, in Colorado, from west to east. No problem. Many slow curves and 7% grades on part of it and 6% on the rest. Top engine coolant temperature was 217, briefly, with 204 to 214 most of the way.
We've also towed I-70 west to east through Colorado over Vail Pass and Eisenhower Tunnel at 11,1xx feet. We did that with a diesel and also a Ford V10 gasser. The V10 was towing a heavily loaded Montana 3295RK and the others were towing this heavily loaded 3400RL.
So long as the curves are not a problem with your length I'd think you'll be fine unless you think the heating problem might cause problems.
Just checked the map. That must be US 24 between I-70 and US 50 at/near Poncha Springs or Salida? My Mountain Directory says on that stretch there is Tennessee Pass (10,424 feet) 5 to 6% grades for most of it and 6% for 3 miles. There's also a 20 mph curve near the top. Also on that stretch is Battle Mountain with 4 miles of 6 to 7% grade with 30 mph curves and two 20 mph switchbacks at the bottom. The other side has 2 to 3 miles of 6 to 7% grades with 30 mph curves. There is no mention of length restrictions on either of those.
That's a pretty good climb but I bet the scenery is fantastic. The temperatures up that high should be pretty moderate but if the engine tends to heat then that might still be a problem.
The picture in my signature was taken at Monarch Pass last week when we stopped for a nature call.
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